A weak solution of the coupling of time-dependent incompressible Navier-Stokes equations with Darcy equations is defined. The interface conditions include the Beavers-Joseph-Saffman condition. Existence and uniqueness of the weak solution are obtained by a constructive approach. The analysis is valid for weak regularity interfaces.
@article{M2AN_2013__47_2_539_0,
author = {Cesmelioglu, Aycil and Girault, Vivette and Rivi\`ere, B\'eatrice},
title = {Time-dependent coupling of Navier-Stokes and Darcy flows},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {47},
year = {2013},
pages = {539-554},
doi = {10.1051/m2an/2012034},
mrnumber = {3021697},
zbl = {1267.76096},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2013__47_2_539_0}
}
Cesmelioglu, Aycil; Girault, Vivette; Rivière, Béatrice. Time-dependent coupling of Navier-Stokes and Darcy flows. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) pp. 539-554. doi : 10.1051/m2an/2012034. http://gdmltest.u-ga.fr/item/M2AN_2013__47_2_539_0/
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